Improved estimation for temporally clustered extremes

In this paper, we investigate the effects of declustering applied to sequences of extreme observations. Through a simulation study, we demonstrate that the common practice of analysing peaks over thresholds (POT) is liable to incur serious bias in the estimation of parameters, as well as the return levels used as design specifications when building to withstand extremes of wind or rain, or river or sea level. We demonstrate that a much simpler approach, the direct analysis of all exceedances of a high threshold, can reduce this bias to negligible levels. This approach has, until now, been unpopular, because the data being analysed are not independent. The effect of this is to cause the standard errors associated with parameter estimates to underestimate the uncertainty attached to these estimates. We employ existing but little-used methodology to inflate these standard errors, and we demonstrate that the adjusted values are very good representations of the true uncertainty associated with maximum likelihood estimates. The overall approach has thus achieved the effect of eliminating the bias in estimation, while accounting for any undesirable effects caused by dependent data. We apply our approach to a sequence of sea-surge data from southwest England, and illustrate the discrepancies between this and a POT approach, which are consistent with the POT approach underestimating long-period return levels. We also pay considerable attention to checking the robustness of our results, demonstrating that the problems of bias caused by the POT approach apply systematically over all of the declustering schemes we consider, as well as over the entire range of tail behaviours. When the primary interest is in return-level estimation, we recommend that our procedure will generally prove to be much more effective and reliable than the POT approach. Should there be a deeper interest in the serial dependence itself, then we recommend that this dependence is explicitly modelled, and we refer the reader to an earlier paper by the authors, published in this journal. Copyright (c) 2006 John Wiley & Sons, Ltd.